ART Iwan Setyawan Perceptual quality Full text

PERCEPTU4L QUALITY OF GEOMETRICALLY DISTROTED IMAGES PART 1: THE
Hf JMOGENITY-BASEJJ PERCEPTUAL QUALITY MEASUREMENT (HPQM)
!won 51erymmn

PERCEPTUAL QUALITY OF GEOMETRICALLY DISTORTED
IMAGES
PART I:
THE HOMOGENITY-BASEI> PERCEPTUAL QUALITY
ｬｦｅａｓｕｒｾｎｔ＠

fHPQM)
Iwan Setyawan
(iwan.setyawanra>ieee.org)

Ab!)·fract

·-.:·

Measurement of the perceptual impact of geometric distortions applied to images or
\ideo on human obsen ers is a difficult and not \Yidely researched subject. As a result.
we are currently stiJJ lacking the proper objectiYe methods to measure the perceptual

quality of such distorted images. In this paper. \Ye propose an objectiYe quality
measurement method suitable for assessing the perceptual quality of geometricaJJy
distorted images. In the second part of this series. we "iJJ eYaluate the proposed
system by performing a user test experiment.
ｋ･ｹｷｯｲｬＮｾＺ＠

Geometric distortion. human Yisual system. perceptual quality
measurement of images

1. Introduction
Geometric distortion has always been a problem in the deYelopment of
watermarking systems. Tllis distortion happens '"hen the \Yatermarked data undergoes
a geometric operation. This can happen due to Yarious reasons. but basicalh
geometric distortion occurs either due to the explicit application of geometric
transformations or as a by-product of other processes (or attacks). Explicit application
of geometric transformation includes non-malicious operations performed by a user.
for example resizing of an image to fit one· s desk:top. and malicious operations for
example application of random bending to an image using tools such as StirMark [ 1].
Examples of processes or attacks that produce geometric distortion as a by-product
are the distortions incurred during the printing and scanning process [2] {due to the

impe1fection.s of the printer and/or scanner) or the distortions in Yideo frames captured

59

Techne Jurnal Ilmiah Elekiroteknika Vol. 8 No. 2 Oktober 2009 Hal 59- 76

using a hand-held camera in a theatre in the digital cinema scenario [3] (due to the
position ofthe camera lens distortions, etc.).
We can also classify geometric distortion based on its locality. In this respect
geometric distortions can be classified as either global or local. In global geometric
distortions. the underlying geometric transformation describing the geometric
distortion applied to the whole image can be described using a single anal)1ical
expressiOn and a smgle set of parameters associated with the expression. ln local
geometric distortions, the underlying geometric transformation uses different
analytical expressions and/or different paran1eter sets for each pru1 of the image.
There are two aspects of geometric distortion that me of interest for the
watermarking coimnunity, namely:

l.l.The watermark de-synchronizing aspect.
Geometric distortion poses a problem for watennru-k.ing systems because it can

de-synchronize the \Yatennark detector. making the watermru-k undetectable. A lot of
reseru-ch effort has been performed in this area \Yithin the watermru-king community.
The reseru-ch effort focusses on three approaches to dealing with this problem. The
first approach is designing \Yatermru-king schemes that are inYariant or insensitiYe to
robust against geometric distortion [4.5]. The second approach inYolves research on
methods (that is independent of the \Yatermark detection) to inYert the geometric
distortion [6,7.8]. Finally, the third approach is to embed a S)nchronization signal in
the \Yatermark. itself to facilitate re-synchronization of the watermark by the
embedder in the eYent of geometric distortion [9].

1.2.

The visual quality degradation aspect.
Geometric distortion degrades the Yisual quality of the" atennarked data. Like

all other distoi1ions that affect "atennru-king systems. distortions due to geometric
transformation are also bounded by the maximum visual quality degradation it can
incur

｢･ｦｯｾ＠

the dist011ed image loses ru1y commercial Yalue. It is therefore important

to be able to measure such distortion. The result of such measurement can be fed back
into the design process of \Yatermru·king systems robust against geometric distortions
Tllis aspect of geometric distortion has not been widely discussed in the literah1re. As
a result. we are currently lacking ru1 objectiYe measure to quantify such distortion.
60

PERCEPTUAL QUALITYOFGEOMETR/CALLY DISTROTEDIMAGES PART/: THE
HOMOGENITY-BASED PERCEPTUAL QUALITY MEASUREMENT (HPQM)
!won Serymnm

Existing objecti,·e Yisual quality assessment tools. for example PSNR are not suitable
to be used to quantify ,·isual quality due to geometric disto11ions because they rely on
the pixel-per-pixel relationship between the original and the distorted images. An
image distorted by geometric transformation loses most. if not alL such relationship to
the original image. Measuring a geometrically distm1ed image using PSNR "ould.
tlwrt>fnre 'ield nn meaningful rFsult

In this paper we address the second aspect of the geometric distot1ion problem
for "atermarking systems We propose a new Yisual quality measurement method
suitable for tlli.s class of image distortion. Our approach is based on our preYious work
[I 0]. In this paper "e limit ourseh·es to the Yisual quality measurement of global

geometric distortions on still images. This paper is organized as follows In Section 2.
''"e "·ill present the underlying hypothesis on "·hich our proposed method is based. In
Section 3. we "·ill present how we test the hypothesis and quantify the geometric
distortion applied to an image. In Section 4. '"e ""ill present the test setup we used to
test our proposed method. as well as the results of our experiments. Finally. in Section
5. '"e will present our conclusions and an outlook for further research.

2. The underlying hypothesis
2.1. Modeling global geometric transformation
The number of possible geometric transformations that can be applied to an
image is essentially limitless. TI1e possibility ranges from simple transformations to
more complex ones. An example of geometric transformations is the RST (rotation.
scaling and translation) transform described by the following equation·

II

(

l= s( cos
sm R

R

v;

- sin R J( X + ( ｾＧ＠
cos R ｾ＠ y
1,

J

J

(1)

Ahernatiyely. an example of more complex geometric transformations is the

bilinear transform described by the follo"ing equation·

(
l

u )\
v

(a

=I\ h

\j (

c j\( x
1..' '\
( g 'i
+
/Xl'+
f) .

h
d ,J')

l)

(2)

61

Techne Jurnal llmiah Elektroteknika Vol. 8 No. 2 Okiober 2009 Hal 59- 76

Due to the Yast number of possible geometric transforms applied to the image.
it is impossible to model each of them individually. There are some approaches that
can be used to soh·e this problem One approach is to use simpler transformation
models. for exan1ple RST or affine transform, to approximate the underlying complex.
global geometric transform [9]. The approach is based on the assumption that a
complex geometric transformation applied on a global scale can be approximated by a
::;unplct iransCurmation mudel applied on

more local "rah'

\nother pnssib'"

approach IS to use orthogonal polynomials to do the approximation [8]. In this
chapter. we use local RST/affine transform to approximate the global underlying
transform

2.2. The hypothesis
At tllis pomt we would like to present our definition of the homvgenelfy of u
global geometric distortion. as follows: A distortion is said to be homogenous
underlying global

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can be approximated h)' one R.\'T or ajfine

with one se1 (:{parameters (.tssoclated 'Yl•ifh

If.

tr the

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The reader should note that from this

definition we make a distinction between global and homogenous distortions. The
first term refers to the locality "ith \\·Jlich we apply the underlying geometric
transformation. \\bile the second term refers to the locality of the approximation of
the underlying global transformation using RST or affine transforms. In other \Yards.
non-homogenotJs distoi1ions must be approximated by multiple local. RST/affine
geometric transforms These local transforms haYe parameters that are Yaf)·ing from
one part of the image to the other.
The following figure presents an original image. along with two distorted
Yersions of the Image The first distorted Yersion (Figure l(b)) ts the result of rotating
the original image by 3 degrees followed by cropping and rescaling. The second
distorted Yersion (Figure l(c)) is the result of applying a complex sinusoid-based
transform to the original image.

62

PERCEPTUAL QUALITY OF OEOMETRJCAT.T. Y TJTSTROTEJ) IMAGES PART l: THE
HOMOOENITY-BASED PERCEPTE4L QUALITY MEASUREMENT (HPQM)
lw£1n Setymwn

(h)

(a)

( lui

liJ.IlSli.lliUH, ｵ･ｾＮＺ｡ｳ＠

Ulll

obse1 \ lli!Ull

111dH.:UleS

Rotation anct Scaling parameters giYe a larger impact on the m erall perceptual

that

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of the image The larger the difference. the lower the score for the block will be This
is because eyen "hen the RST/affine transformation of a block can be

ｰ･ｲｦ｣ｴＡｾ＠

estimated (i.e . zero residual error). such a block can still heaYily influence the m erall
perceptual quality of the image if the local RST/affine transformation is seYere. The
parameter {), and the 'Yeighting factors of the RST/affine parameters are determined
experimentally. Finally. the calculation of the final score is normalized so that the
ma:ximum score that can be achieYed by an image is 100.

(a)

(h)

Figure 3. E.-ramples n(the quadtree structure

As a fmal note. "e "ould like to point out that the quad tree structure examples
111

Figure 3 sho'Y hmY the image content influences the measurement procedure. as

already pointed out in Section 3.2. In this example "e can see that areas "ith a lot of
texture or structure are more accurately approximated and finely partitioned compared
to the flat areas or areas "ith less details although they undergo similar distortion. As
a consequence, flat areas are gi Yen higher scores than more detailed areas.

1

·nwt is. "hen there is zer'' wtntion and sheanng. s..:almg fador of 1 and zero translatJOII

Technc Jurnnl Ilmiah Elektroteknikn Vol. 8 No. 2 Oktober 2009 Hal :'i IMAGES PART/: THE
HOMOliEN/1'1'-BASEO PERCEPTUAL (JUAL/l'Y MEASUREMENT (HPQM)
!wan !)etyawan

Table 1. Geometric distortions used in the e:xpenmenf
ﾷＭｾＺ

Description
---

AJ

No distortion (original image)

A1o

Sinusoid (stretch-shnnk). scalmg factor l. 0.5 penod

Au

Sinusoid (stretch-shrink). scaling factor L 1 period

-

1

Ar

ＭﾷＢｾ

, Sinusoid (stretch-shrink).

ＭﾷｾＮ＠

...
Ｍｾ＠

-

v_ ............

I

An

Sinusoid (stretch-shrink). scaling factor 3. 1 period

Au

Sinusoid (increasing fi·eq). amplitude factor

=

0.2. starting period

=1.
freq increase factor

4

Sinusoid (increasing freq). amplitude factor= 02.

A 1,

=L
freq increase factor= 9
Sinusoid (increasing amplitude). start amplitude factor = 0.1. 5

ｾﾷＭＱｰ･｟ｲｩｯ､ｳＬ＠

amplitude increase factor 4
Sinusoid (increasing amplitude). start amplitude factor = 0. L

41

L

1

periods. amplitude increase factor

ｾｉ＠

I

9

The distottions chosen for the test set range from distortions that are
perceptually not disturbing to distortions that . A 13 l distort the image by locally stretching
and shrinking the image. Depending on the image content this kind of distotiJOn may
not be percept1wlly disturbing. The rest of the distortions distorts the image by

usible. eYen "hen the se\ ･ｲｩｴｾ＠
distortion se\ ･ｲｩｴｾ＠

is lo". The distortions :A:. A 3,

A 5 l apply the same
ａｾＮ＠

mer the "hole image. "hile the seYerity of distotiions [AJ./. A 1_,

A,(,, A 1 -: is Yaried "ithin the image. Some examples of the geometric distortions used

in the experiment are sho\\ n in Figure 5.

-t

i

Ｑｾ＠

;

ｾＱＭＮ＠

,_ T
\

--

I

I

(
ｾＭ

-t--- --: ---

I

ｾＭ

-

).

ｾＭ

--r-

Ｍｾ

; -)--i-

___;;;.,,- --'.

Ｍｾ＠

-:---- ｾ＠ --

ＭｾＮ

jl

ｾ｜＠
'-

I
I

ＭｾＱ＠

(u}

(h)

(c)

Figure 5. Examples o(lhe geometric distortions:
(a) Distortion A5, (h) Distortion A13 and (c) lJistortion A 11,

Finally. to gtYe an early indication of the performance of the proposed method.
we also perftJrm PSNR measurements of the images and a preliminary subjectiYe test.
A more detailed companson of the performance between the proposed method and
other objectJ' e test methods "ill be described in the next paper. Ltke" ise. a more
detailed uset test expenment "ill also be descnbed m the next paper.

PERCI:PTU4L OU4UTY OF (;EOMETRICALLY DISTROTED IMAGES PART 1: THE
HOMlJUENITY-BASED PERCEPTUAL QUALITY MEASUREMENT (HPQM)
]wan ,\'eryawnn

Table 2. HPQM scores and PSNR values
Bird
HPQM Score

Kremlin

· .• ·PSNR (dB) ··
.r.

ｊｾ･＠

Image

Score

AI

100

Al

'J3.'J.)

A3

. Score

•HPQMSeore
.
·.'" Score
IllUlge,,

PSNR(dB)
Image

Score

..,.

Al

100

Al

I

A2

29.33

A2

78. PER( 'EP1VAL QVAUTY MEA.'iUREMENT (HPQM)
!wan Setymran

design and analysis of a more elaborate user test experiment will be described
in the next paper of the series.
The proposed system is still a work in progress and currently there are still
some limitations that should be addressed. The improYements of these limitations are
the topics for our future works. In particular. \Ye think that the following topics should
l>t: 111\t:SlJgaied mute lhoroughh.

1. Refinement of the procedure used to determine distortion homogeneity. The

discriminating po"·er of the objectiYe test scores is fmrly small (see Table 2 ).
This could be due to the discriminating po"er of the equations "e use to
compute the final score being too small or due to the chosen Yalues of the
parameters used in the equation being not Yet optimal Further research should
be conducted to inYestigate and improYe the performance of the method in this
respect.
2. Take image content more into account since human perception of geometric
distortiOn is highly influenced by the presence of certain structures in the
image. In our experiments. this aspect has been indirectly taken into account
due to the fact that our distot1ion homogeneity measurement procedure is
influenced by image content. HoweYer. further UlYestigation should be
performed to find ways to explicitly imolYe the image content in the final
score calculation.

6. References
F.AP. Petitcolas. RJ. Anderson and M.G Kuhn. Attacks on copvright markmg
in Information Hiding: 2"d Int Workshop (lecture Notes in Computer

'>J'Stcm·chemej(Ju/tgllal cmema.in
Proceedings of lEEE. IClP 200 L pp 487-4!N. Thessa!onikL 200 I

75

Tcchnc Jurnal llmiah Elcktrotcknika Vol X No. 2 Oktober 21109 Hal

4. J.J. K.

6 Ru:maidh and T.

"i() -

7(,

Pun. RotMion. scale and translation invurwnt d1gital

image l-l'afermarking. in Proceedings ofiEEE. ICIP 1997. pp. 536- 539. Santa
Barbara. CA. 197
5. I. Sety